While it may seem like a simple idea, developing new weaponry in X-COM: Enemy Unknown can make or break your team in the middle stages of your campaign against the enemy threat. With the council watching over you, the stakes are higher then ever. Let's look at the weapon tiers:
The starting weapons rely on human technology. While these arms will certainly suffice in the beginning of the campaign, they won't hold up for long. Players will find that multiple soldiers will have to concentrate fire on a single opponent to do significant damage. Luckily, you won't have to waste much time in researching Laser weaponry….
As you develop laser rifles, scatter guns, heavy lasers and the laser sniper rifle, you'll find that your soldiers will benefit from increased accuracy and damage. The laser guns also have some kickass sound effects. Burning a few mutons faces off makes the laser sniper rifle well worth the cost.
As soon as possible, research and upgrade to laser weaponry. It will give you an immediate leg up on the competition. The more UFOs you assault, the more terror attacks you fend off, the more powerful the aliens will become. Researching and equipping this new weaponry will help keep your forces in lockstep.
It's probably more important to give your assault class soldier a laser scattergun than it is to give your sniper soldier a lazier rifle. Why? There'll be a longer gap between laser scattergun and alloy cannon than bullet and plasma sniper rifles.
Plasma represents the peak in weaponry for many of your soldiers, notably the heavy and sniper classes. As soon as it is available, research and deploy plasma weaponry to these classes. You can let some of your soldiers keep their human pistol sidearms to finesse enemy health down to ARC-able levels, but for the most part your team should move on to the new tech.
Heavy's will not only gain increased accuracy, but their weaponry will decimate smaller aliens. Thin Men and other small fries will run in fear, but the alien forces will quickly upgrade to armor and other types of heightened defenses.
Use your sniper's plasma rifle bolts to put holes in their head while the heavy's hold up the front line. Plasma weaponry should not be sat around on. When you're able to research, put it on top of your list and set the engineers to building.
Alloy Cannons and Guided Fusion Launchers:
If you're like me, an assault class soldier with ghost armor is as deadly a weapon as you have in your arsenal. The alloy cannon further sharpens the tip of your squad's spear.
The same goes for the Guided Fusion Launcher, a weapon only researchable after taking down the Battleship-class UFOs later in the game. I haven't found these to be as necessary as equipping the rest of my soldiers with new weaponry. Leave the Guided Fusion Launcher for last (if you haven't gotten around to beating the game yet).